Apparatus and method for mitigating range-doppler ambiguities in pulse-doppler radars

Abstract

A method and apparatus for resolving Doppler frequency shift ambiguities in pulse Doppler radar systems provides a radiated signal that is modulated with a periodic waveform having a plurality of pulses within a period, the interpulse intervals between pulses in the period being unequal. Radar target returns are autocorrelated for a plurality of lags, which may include the interpulse intervals and linear combinations thereof. The calculated arguments θ Ci of the autocorrelation function are unwrapped by adding 2k.sub.π, k=0, ±1, ±2, . . . , to the phase θ C1 obtained for the shortest lag T 1 and determining an integer m k2 from |(θ C2 +2m k2 π)-(T 2 /T 1 )θ C1 | <π and then setting θ 2 =θ C2 +2m k2 π. Phase angles θ 3 , θ 4 , . . . , θ m are unwrapped in a similar manner, the integer m ki being determined from |(θ Ci +2m ki π)-(T i /T i-1 )θ Ci |<π. The unwrapped phase angles and the point (0,0) are least mean square fitted to lines of phase angle vs lag for each value of k. The root mean square error of the phase angle offset from each line is determined and the slope of the line with the minimum RMS error is chosen as the Doppler frequency shift from which the velocity of the target is extracted.

I claim: 
     
       1. A Doppler radar of the type having a stabilized transmitter for transmitting pulse modulated signals and a receiver for receiving radar returned signals further comprising: waveform generator means coupled to said transmitter for providing a periodic modulating waveform, each period including a plurality of pulses positioned with unequal intervals therebetween, thereby causing periodic pulse modulated radiated signals with each period having a plurality of radiated pulse modulated signals with unequal intervals therebetween;   correlation means coupled to said receiver for performing autocorrelations of returned radar signals, lags for said autocorrelations being equal to said unequal intervals between said plurality of pulses positioned in said period, and for providing signals representative of said autocorrelations, said autocorrelations having an amplitude and a phase; and   Doppler frequency shift means coupled to receive said autocorrelation representative signals for providing signals representative of Doppler frequency shifts of said returned radar signals.   
     
     
       2. A Doppler radar in accordance with claim 1 wherein said Doppler frequency shift means comprises: means coupled to receive said autocorrelation representative signals for providing signals representative of said phase angles of said autocorrelations; and   frequency shift means coupled to receive said phase angle representative signals for providing signals representative of said Doppler frequency shifts.   
     
     
       3. A Doppler radar in accordance with claim 2 wherein said phase angle means comprises: means coupled to receive said phase angle representative signals for selecting a k value and adding 2kπ, k=0, ±1, ±2, ±3, . . . , to a first phase angle θ C  (T 1 ) to obtain an augmented first phase angle representative signal, said first phase angle θ C  (T 1 ) being said phase angle of an autocorrelation for lag T 1  ;   means coupled to said correlation means to receive at least one autocorrelation phase angles θ C  (T j ) respectively obtained for lags T j , j+1, for determining an integer m kj  for each phase angle θ C  (T j ) where m kj  is determined from ##EQU8## and to provide signals representative of said at least one augmented phase angles θ C  '(T j )=θ C  (T j )+2m kj  π;   line means coupled to receive said augmented first phase angle representative signal and said at least one augmented phase angles representative signals for determining a least mean square fit of said augmented first phase angle and said at least one augmented phases angles to a straight line passing through an origin of a phase angle vs lag coordinate system for each selected k value, and for providing signals representative of said straight lines respectively corresponding to said k values;   evaluation means coupled to receive said augmented first phase angle representative signal, said at least one augmented phase angles representative signals, and said straight lines representative signals for determining root mean square (RMS) offset error of said augmented first phase angle and said at least one augmented phase angles from each of said straight lines and selecting that one of said straight lines with a RMS offset error that is less than RMS offset errors of all other straight lines, thus providing a selected straight line with minimum RMS offset error, said selected straight line having a slope representative of Doppler shifted frequency due to a velocity of a scatterer from which radar return signals emanate, and for providing a signal representative of said selected straight line; and   slope means coupled to receive said selected straight line representative signal for determining said slope and for providing a signal representative thereof.   
     
     
       4. A Doppler radar in accordance with claim 3 further including means coupled to said slope means for determining velocity of said scatterer from said slope. 
     
     
       5. A method of determining velocity of a moving target comprising the steps of: radiating a signal modulated by a periodic waveform, each period of said periodic waveform including a plurality of pulses positioned with unequal intervals therebetween;   autocorrelating received backscattered returns from said target using lags equal to said unequal intervals to obtain autocorrelations of said received backscattered returns for lags equal to said unequal intervals, each of said autocorrelations having an amplitude and a phase; and   utilizing said autocorrelations for determining target velocity.   
     
     
       6. A method in accordance with claim 5 wherein said utilizing step includes the steps of: extracting said phase angle from each of said autocorrelations to provide extracted phase angles; and   processing said extracted phase angles to obtain said target velocity.   
     
     
       7. A method in accordance with claim 6 wherein said processing step includes the steps of: adding 2kπ, k=0, ±1, ±2, ±3, . . . , for a selected k value to a first phase angle to obtain an augmented first phase angle said first phase angle being said phase angle of an autocorrelation for lag T 1  ;   determining an integer m kj  for at least one autocorrelation phase angles θ C  (T j ), respectively obtained with lags T j , j≠1, and providing signals representative of at least one augmented phase angles, θ C  '(T j )=θ C  (T j )+2m kj  π, where m kj  is determined from; ##EQU9## determining a least mean square fit of said augmented first phase angle and said at least one augmented phases angles to a straight line passing through an origin of a phase angle vs lag coordinate system for each selected k value, thereby providing a plurality of said straight lines respectively corresponding to said k values;   calculating a root mean square (RMS) error of said augmented first phase angle and said augmented at least one phase angles for each k value corresponding straight line;   selecting that straight line with a RMS offset error that is less than RMS offset errors of all other k value corresponding lines, thus providing a selected straight line with minimum RMS offset error, said selected straight line representative of autocorrelation phase angle versus lag and having a slope representative of Doppler frequency shift due to said target velocity; and   determining said target velocity from said Doppler shift.